Specification Testing in Nonparametric Instrumental Quantile Regression

Abstract

In econometrics, there are many environments which require nonseparable modeling of a structural disturbance. In this setting, the case of possibly endogenous regressors has been studied recently. Regarding this literature, key assumptions to obtain identi fication and estimation results are: Valid instruments must be at hand and the model must be monotonic in the nonseparable, continuously distributed scalar disturbance. If one of these assumptions is violated a function solving the model equation need not to exist. In this paper we consider a test of whether such a function exists. Our test statistic is asymptotically normally distributed under correct speci cation and consistent against any alternative model. Under a sequence of local alternatives the asymptotic distribution of our test is derived. Moreover, uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases. In Monte Carlo simulations, we study the fi nite-sample power of our test against different alternatives. As an empirical illustration we consider a quantile regression model describing the e ffect of class size on scholastic achievement.